Archive for May, 2011

Last time I discussed knowledge and pointed out that knowledge was often attacked as rote memorisation of facts. I accepted that if children do simply learn to recite facts it is inadequate as a model of education. However, when we look at what is missing from this model we don’t necessarily find any reason to dismiss the importance of memorisation, let alone the entire concept of knowledge.

The first point I will make is that nobody argues for rote learning in the strictest sense. If “rote” refers to the situation where information is passed on without understanding (and “understanding” is a grasp of meaning, knowledge of underlying structures and abstract concepts and a facility that allows for facts to be applied in different contexts) then rote learning has no advocates. The most untiring advocate of memorising the spellings of individual words would still want students to be able to understand and apply the phonetic meaning of letters. The staunchest proponent of drilling times tables into kids would still want them to understand what it means to multiply and to be able to solve problems with it. The most enthusiastic supporter of chanting conjugations of verbs would still want their students to understand where each conjugation was to be used and, eventually, to master their use in actual sentences. Nobody deliberately plans to sideline all understanding.

Where approaches do differ is in how much priority should be given to understanding. Some approaches appear to suggest either that it can be taught independently of passing on information, or that the endeavour of teaching understanding is in opposition to teaching knowledge. I would reject the latter claim outright, simply on the grounds that knowledge as a concept includes understanding rather than just acquisition of facts (and in this I am simply repeating the point I attributed to Newman last time). But the more plausible argument is the former one: that understanding can occur and be taught in the absence of memorising any information at all.

The first objection to this is empirical: that it doesn’t fit what we know about how the mind works. To quote my favourite cognitive psychologist (Willingham, 2009) :

Understanding is remembering in disguise… It’s often difficult for students to understand new ideas, especially ones that are really novel, meaning that they aren’t related to things they have already learned. What do cognitive psychologists know about how students understand things? The answer is that they understand new ideas (things they don’t know) by relating them to old ideas (things they do know).

This is why it is easier to understand a text about something you already know about rather than something you are unfamiliar with. This is why it is often easier to learn by analogy. This is why students understand that

“How many 2 pint jugs can be filled from an 8 pint barrel?”

is a division problem faster than they realise that

“How many 1⅝ pint jugs can be filled from a 7⅚ barrel?”

is a division problem, despite the two problems being identical in their basic structure.

It is also the case that knowing information well, so that it can be recalled “automatically” i.e. without much cognitive effort, frees up the mind for other forms of thinking including those involved in developing understanding. This is because, as Willingham (2009) explains:

Finding a fact in long-term memory places almost no demand on working memory. It is no wonder that students who have memorised math facts do better in all sorts of math tasks than students whose knowledge of math facts is absent or uncertain. And it’s been shown that practicing math facts helps low-achieving students do better on more advanced mathematics.

This is worth bearing in mind when confronted with arguments like that of Gardner (2004) who identified a lack of understanding of concepts in students with an overemphasis on basic skills and rote. It is equally possible, and empirically more probable, for a lack of deep understanding of underlying concepts to result from weaknesses in basic skills and knowledge preventing any depth of thought about the underlying concepts.

The second objection to separating knowledge and understanding is philosophical. We can conceptualise knowledge in ways that are useful but incompatible with the idea that we can separate the concepts of knowledge and understanding. Two ways of doing so are described below.

Dearden (1969) describes “one’s understanding of one’s situation in the world” as being made up of a basic ingredient of ‘forms of understanding’:

…a ‘form of understanding’, which immediately shows itself to be a notion connected with knowledge and experience… There are two aspects of forms of understanding which are important here. First, they are systems of interconnected concepts and organising principles. Secondly, they have distinctive validation procedures for determining the truth, rightness or adequacy of various statements or judgements to be made.

He clarifies this further, rejecting the idea that understanding could be “a single, monolithic and undifferentiated whole” or “a matter of good attitudes, together with possession of a universal information getting skill.” Most interestingly of all, is how he identifies and rejects a theory of knowledge which is incompatible with this.

The ‘rucksack’ theory of knowledge is the theory that knowledge is just a jumbled mass of information such as might be exhibited to advantage on a quiz programme. The two relevant features in the analogy are that rucksacks can be more or less full, and that they can be loosely carried behind. The knowledge embraced in a form of understanding, however, is organised, well-founded, and so ingredient in the mind so as to transform, not just supply more information about, one’s experience.

In Dearden’s model understanding is the way in which knowledge is organised and used within then mind; it is not something that can replace the learning and recall of knowledge.

A second useful model is that of Oakeshott (1965) who identified knowledge as consisting only partly of information. He defined information in the following way:

It is a set of facts (specific intellectual artifacts), not opinions; it is stated in propositions; it is received on authority; it is capable of being forgotten and it needs to be recollected; it appears in rules to be followed-rules which must be known and recollected in order to perform…there is in all knowledge an ingredient of information. It consists of facts which may range from the recognitions and identifications in which knowledge of any sort emerges from indeterminate awareness, to rules or rulelike propositions which inform the skills and abilities in which we carry about what we may be said to know, and which are sometimes, but not always, expressly known and followed.

This is a broad enough definition of information, that we cannot easily separate information from understanding. Much of what we might class as part of understanding (abstract rules, the identification of underlying structures) fits within this definition of “information”. Oakeshott describes the remaining part of knowledge as “judgement” not understanding. This is where we “know how to do something without being able to state explicitly the manner of acting involved”. This is more clearly part of mastery of a subject than understanding is. A lot of what we call understanding can simply indicate memorisation of abstract information, or worse, repetition of a generalisation. Judgement is a far more useful concept, in that it cannot turn out to be simply another type of memorised fact, but can be readily distinguished from facts.

This is useful because we can now see exactly what difficulties we have when we try to remove facts from teaching. Whereas it might be possible to believe that a lesson with little content was teaching understanding, it is very difficult to believe that it is teaching judgement. In fact it is hard to see how judgement can be taught at all. Oakeshott’s answer is to claim that information and judgement “can both be communicated and acquired but not communicated and acquired separately”. It is taught and learned but is not part of explicit instruction, it is “a by-product of acquiring information…if it is taught it must be imparted obliquely in the course of instruction.” In Oakeshott’s model there is more to the intellect, more to knowledge than knowing information, but the teaching of information is never absent from the teaching of knowledge.

Now I realise this has been a rather long discussion of information, understanding and knowledge, but I hope I have communicated that the simplistic suggestion that we can choose between teaching understanding and teaching facts lacks compatibility with both psychological realities and with more philosophically sophisticated understandings of the concept of knowledge.